Framing a modelling application for Environmental
Problem Solving
Coding Concepts
Learn by example
- Pay attention to the documentation and syntax of
compute_diversity.R
What is a model
understanding
prediction
communication
You are doing this all the time - there are many reasons to make this
process explicit (computer aided modeling)
Basic components of models
Inputs: Varying; think x of a x vs y regression
Parameters: single values that influence relationships in the
model
Transfer Function (model): Equations that transfer inputs to outputs
given parameters
Outputs: what you want to estimate
What’s in the box
What are the processes/relationships that you think are important
to translate inputs to output
Transfer function (mathematical representation)
Parameters, values that influences how the model relationships
work
There are often multiple “boxes” internal to a model
What’s in the box
Often more complicated than a simple regression…
So we need to think through what the relationships are; the processes
are that we want to take in to account
Conceptual models are a good place to start
Conceptual models of the hydrologic cycle
Precipitation = Evapotranspiration + Change in Storage
P = ET + ΔS
(at global scales ΔS includes streamflow since that water is still
“stored” in the earth
Conceptual Hydrology Model - more complex, multiple boxes
Goal - estimate streamflow fromm multiple source (surface and
subsurface)
SERI-Fire
Types of Model
There are many different ways to classify models
A useful classification looks at how models deal with space,
time, and process
Useful because the type of model will have implications for
how you build and use/run the model
Stochastic - Deterministic
Stochastic: Model output is the probability of flood events of a
magnitude greater than 500 m3/sec given rainfall probability
distribution (artificial or generated from data) for a 100km2 watershed
Deterministic: Model output is the depth of flood given a rainfall event
of 10cm over a 100km2 watershed
source
Lumped …Spatially distributed
Lumped - single point in space, or space doesn’t matter
Spatially distributed - model is applied to different “patches” in
space spatial units are independent
spatial units interact with each other
source
Static- Dynamic Time Varying
Static - Processes or Variables modeled do not evolve with time
Dynamic - model elements evolve through time - and variables/results
at one time step typically depends on previous time step
source
Abstract - Physically/Process based
Abstract - relationship between inputs and output depends on
parameters that don’t necessarily have a physical meaning
Physically based - parameters do have a physical meaning (could be
measured) - relationships derived from first principles (theory) of how
things work
Conceptual models: Composing
Pictorial representation of how you think about your system, and what
needs to be included in the model to answer your questions (or achieve
your modelling goal)
There are many software tools available for generating conceptual
models, I like
[Diagrams.net]{https://www.diagrams.net/}
Conceptual model design
Some model designers uses standard symbols for the different model
components
Building Models 
• PhD of Norman Crawford under supervision of Ray K Linsley at
Stanford University in 1962
Conceptual Models 
From conceptual model to flow chart/workflow
Impact of smoke from fires on health of agricultural workers What is
’smoke” What is “health” What is an “agricultural worker”. …leads to
your conceptual model
Design/Selecting Models
What are your inputs-outputs
What’s in the box (the model itself) that gives you a
relationship between outputs and inputs
Transfer function
Parameters, values that influences how the model relationships
work
Types of Models
Conceptual………….Mathematical
Stochastic………….Deterministic
Lumped………….Spatially Distributed: SPACE
Static………….Dynamic : TIME
Abstract………….Physically/Process Based
but biggest differences may often be the degree specific
processes/parameters are accounted for
Types of models: Example
Input: Reservoir height (height) and flow rate (flow)
Output: Instantaneous power generation (W/s)
Parameter: Reservoir Efficiency (K)
Conceptual model
Types of models: Example
Input: Reservoir height and flow rate
Output: Instantaneous power generation
(W/s)
Parameters: K Efficiency , ρ (density of water),
g (acceleration due to gravity)
P = ρ * h * r * g * K Efficiency;
P is Power in watts, ρ is the density of water (~1000 kg/m3), h is
height in meters, r is flow rate in cubic meters per second, g is
acceleration due to gravity of 9.8 m/s2, K Efficiency is a coefficient
of efficiency ranging from 0 to 1.
This is a static (one point in time), deterministic, lumped (one
place) model; its more or less physically based
Types of models: Example
If we expand the model to compute power production over a year, where
inputs were streamflow into the reservoir - Dynamic Model
If we expand to model power production from all the reservoirs in
California, accounting for spatial patterns of snowmelt inputs and
upstream-downstream relationships - Spatially Distributed
Model
If we modified the model to estimate the probability distribution of
power production, given a probability distribution of reservoir levels -
Stochastic Model
Pair and Share
With your conceptual model from Tuesday’s class -
- discuss what type of model you have
- consider that for some conceptual models you might translate/expand
the basic conceptual models into different types of models - discuss
that this might look like for your models
STEPS: Modeling for Problem Solving in ES
Clearly define your goal (question you want to answer, hypothesis
you want to test, prediction you want to make) - as precisely as
possible
Develop a conceptual model - draw it!
Design or Select your
model
Implement the model
Evaluate the model and quantify uncertainty
Apply the model to the goal
Communicate model results
Steps for Design and Implement your model
Design conceptual model
Translate conceptual model into a mathematical
representation
Choose programming language
Define inputs (data type, units)
Define output (data type, units)
Define model structure
Write model
Document the model (meta data)
Test model
Assignment 2
For this assignment you will work in pairs
Your goal is to develop a conceptual model of almond yield - the goal
will be able to predict how almond yields might change if seasonal
precipitation or air temperature patterns change in California - we’d
like to know mean, minimum and average yield anomolies given a climate
prediction
The Lobell et al. 2006 paper will be the source for your model;
specifically look at the equations in table 2.
Draw a conceptual model to represent your model that will
translate inputs to output, with parameters that shape the relationship
between inputs an outputs - on your diagram list what your inputs,
parameters and outputs are with units
Write a simple R function that implements your conceptual
model
Run your model for the clim.txt data that is
posted on Canvas
We will build on this on Tuesday’s class
Grading Rubric
Conceptual model (30 pts)
- correct inputs and output and parameters shown on the diagram (10
pts)
- clear diagram (10 pts)
R Implementation (30 pts)
Extra Credit - a diagram that that works for all tree yields (20
pts)
